Worksheet: Complementary Events

In this worksheet, we will practice finding the probability of complementary events.

Q1:

A bag contains 6 red balls, 8 yellow ones, and 4 black ones. If a ball is randomly selected, find the probability of it being NEITHER black NOR yellow.

A13

B29

C59

D49

E79

Q2:

A class in a school contains 38 students. At the end of the school year, 28 of the students passed mathematics, 32 passed science, and 26 passed both science and mathematics. If a student is chosen at random from the class, what is the probability that they failed science?

A619

B1619

C519

D1419

E319

Q3:

If the probability of an event happening is 1130, what is the probability of the event not happening?

A1930

B23

C35

D1730

Q4:

If the probability that a student passes an exam is 39%, what is the probability that the
student fails?

Q5:

What is the probability of the pointer landing on a section which is not green on the
pictured fair spinner?

A12

B59

C34

D58

Q6:

The probability of a getting a head when flipping a biased coin is 0.56. What is the probability of getting tails when flipping the coin?

Q7:

A box contains 56 balls. The probability of selecting at random a red ball is 57. How many balls in the box are not red?

Q8:

If the chance of Daniel bowling a spare is 8 out of 10, determine the probability of him missing the spare.

A45

B0

C1

D15

Q9:

The table represents the data collected from 200 conference attendees of different
nationalities:

Speak Arabic

Speak English

Speak French

Total Sum

Man

45

35

45

125

Woman

40

30

5

75

Sum

85

65

50

200

Find the probability that a randomly selected participant does NOT speak English.

Q10:

If the chance of hitting a specific target on a dart board is 49%, what is the probability of hitting any other target?

Q11:

If the probability that a football team wins the national league in a country is 0.254,
what is the probability that the team does not win?

Q12:

Suppose 𝐴 and 𝐵 are two events. Given that the probability of 𝐴 or 𝐵 occurring is 0.67, find the probability that neither 𝐴 nor 𝐵 occurs.

Q13:

A bag contains 4 red, 3 green, 5 blue,
and 9 yellow marbles. If a marble is randomly chosen from the bag, what is the probability of choosing a marble which is not blue?

A521

B17

C67

D1621

E47

Q14:

The probability that a student passes their mathematics exam is 0.73. What is the probability
that they fail?

Q15:

Suppose 𝐴 is an event with probability 𝑃(𝐴)=1419. Determine 𝑃𝐴.

A719

B1419

C519

D419

Q16:

The probability that an event occurs is 211. What is the probability that the event does not occur?

A911

B119

C112

D92

E211

Q17:

A survey of 48 students reveals that 28 of the students prefer playing football and 11 prefer basketball.
The rest of the students prefer tennis. If a student is chosen at random, what is the probability they prefer tennis?

A316

B3148

C3187

D329

Q18:

A class has 45 students. The probability of choosing at random a student whose age is 10 or less is 23.
How many students in the class are older than 11?

Q19:

A factory produces 9,000 shirts each day. At the end of a day, 500 shirts were inspected and 18 were found to be defective. What is
the expected number of shirts produced that day that will not be defective?

Q20:

Suppose 𝐴 and 𝐵 are two events. Given that
𝑃(𝐴)=110, 𝐴⊂𝐵, and
the probability of only 𝐵 occurring is 0.35,
find the probability that 𝐵 does not occur.

Q21:

According to a survey, 24 out of 120 school students prefer
reading comic books. In a school of 500 students, how many
are expected not to prefer comic books?

Q22:

Suppose 𝑆
is the sample space of a random experiment. Given that 𝐴⊂𝑆
and 𝑃𝐴𝑃(𝐴)=23, find 𝑃(𝐴).

A35

B13

C25

D23

Q23:

A coin is tossed 700 times. Given that heads appeared 353 times, how many times did
tails occur?

Q24:

A survey asked 112 students from a school what sport they prefer and the
results are shown in the table.

Favourite Sport

Football

Handball

Athletics

Tennis

Basketball

Number of Students

27

40

9

29

7

Find the probability that a student does NOT prefer athletics. Round
your answer to 3 decimal places.

Q25:

There are 18 boys in a class of 33 students. If a student
is selected at random, what is the probability of the student being a boy?